"Those guys continue to come in and get the job done," White Sox manager Robin Ventura said.
After the Dodgers rallied to tie the game with four runs against Humber in the third, Alexei Ramirez scored the go-ahead run in the fourth. He was hit by a pitch by Dodgers starter Chad Billingsley, stole second, advanced to third on an error and scored when Alejandro De Aza grounded into a forceout.
The National League West-leading Dodgers (41-25) didn't have a hit after the fourth inning.
"We are down 4-0 there and to get back in the game I thought it was a huge momentum swing," Dodgers manager Don Mattingly said. "But then to give that one run right back, we let that momentum get back on their side.
"Still at that point, we had a lot of ballgame left. At that point, I'm thinking it's going to be two bullpen games with a chance of putting some runs on the board. They get that run, and we weren't able to score the rest of the night."
The White Sox (35-30) escaped trouble after issuing walks to lead off both the seventh and eighth innings. Santiago walked Elian Herrera to begin the seventh, but he struck out Andre Ethier. Jones entered and struck out Jerry Hairston Jr. and got Bobby Abreu to pop out to end the inning.
Crain issued a leadoff walk to A.J. Ellis in the eighth, but pinch-runner Tony Gwynn Jr. was caught stealing to end the inning.
Humber (3-4) earned his first victory since May 29 and his second since his perfect game on April 21. He allowed four runs and nine hits -- all singles -- in five innings, striking out four and walking two.
The Dodgers tied the game at 4 with a four-run third. Billingsley's leadoff single began the rally and James Loney's two-out single scored the tying run.
After relinquishing the four-run lead, Humber threw two scoreless innings.
"It's not his best [outing]," Ventura said. "[He] battled his way through it, and he gave us an opportunity to win."
Humber also collected his first Major League hit, an RBI single that extended the White Sox lead to 3-0 in the second inning following Ramirez's two-run single.
"Fortunately, we scored some runs," Humber said. "I got in on the act a little bit, so that was nice. It was a good win."
Humber has given up at least four runs in four of his last five starts.
"I felt like I pitched pretty well," he said. "As long as it's good enough to get a win for the team, that's good enough for me."
Dropping to 1-3 at home and 4-5 overall, Billingsley gave up five runs (four earned) and eight hits in six innings. He also recorded two singles off Humber.
"I faced them quite a bit in Spring Training," Billingsley said. "I think it was two or three times. There's no secrets. I've faced them in the past, too."
After hitting two home runs Friday, Alex Rios hit an RBI triple for a 4-0 White Sox lead in the third.